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9.2.4.7 Transformer Selection and Design

After determining the value of current sense resistor RCS, determine the maximum peak current at maximum demand point on the modulator. Accommodate for the IPEAK adjustment for frequency dithering. Use this value when calculating the margin for core saturation. In this case, IPK(sat) calculates to 4.13 A.

Equation 29.

In subsequent calculations of required primary turns etc, the average maximum peak current, IPK(max) , during the frequency dither period should be used, which calculates to 4.0 A.

Equation 30.

Knowing IPK(max), LPRI and the turns ratio, the choice of transformer size and core shape and type dictates the required number of primary, secondary and bias turns, and the size of the air-gap. Various trade-offs, design preferences, and transformer design targets (size, cost, target losses, etc.) influence the specific choice of transformer core in any given design.

In the case of the UCC28630EVM-572 (PWR572 EVM), core area-product geometry was used to choose the minimum core size available to meet the power level. The core geometry factor Kg is a figure-of-merit that reflects the core power capability, in terms of its physical size, shape and design. It combines the core effective cross-sectional area, Ae, winding window area, Aw, and the mean length per turn (MLT) of wire around the core.

Ku is a winding window utilization factor that accounts for the percentage of the window that is occupied by Copper

Ku can often be as low as 25%, due to the fill factor (gaps between wires), wire insulation (especially for triple-insulated wire), and the need for insulating tapes and EMC shielding layers. The estimate of the required core geometry needs an estimate of the aggregate total winding current ITOT. The analysis models the flyback transformer primary and secondary windings as a single lumped non-isolated inductor (such as a single winding buck inductor), only for the purpose of sizing the required core winding window to achieve the target copper loss. In this case, the secondary-side current amplitude reflects to the primary side so that aggregate total primary current. ITOT can be estimated in Equation 33.

Equation 33.

where

d is the primary on-time duty cycle

dSEC is the secondary-side flyback period duty cycle

At rated power and minimum bulk capacitor voltage, the inductance LPRI has been chosen to achieve boundary-mode conduction, therefore the duty cycle is given in Equation 34.

Equation 34.

and

Equation 35.

At the boundary conduction point, the primary peak current IPK is at the level set by the modulator, VCS(bcm). So from Equation 33, ITOT becomes Equation 36.

Equation 37 indicates that this design requires a core size and shape with a KG of more than 6.9 × 10-12. A review of commonly used cores indicated that the RM10/I core set meets this requirement. With Ae of 96.6 mm2, Aw of 44.2 mm2 and mean length per turn (MLT) of 52 mm, KG(RM10) is 7.9 × 10–12, giving some margin over the design target.

Equation 38.

With the chosen core, the actual primary, secondary-side and bias turns can be calculated. The required primary turns depend on the allowed Bmax. For most power ferrites, a value in the region of 315 mT is commonly used.

Equation 39.

Round NP to 34. Now the required secondary-side turns can be calculated, using the previously calculated turns ratio per Equation 23.

Equation 40.

Again, NS is rounded to 6. Due to the integer rounding of the turns count, ensure that the actual turns ratio is within 5% of original target (if outside this range, secondary-side rectifier or primary MOSFET stress may be too high).

Again, NB is rounded to 4. The effect of integer scaling in the turns is verified by calculating the expected bias voltage versus target.

Equation 43.

The VBIAS target was 12 V, so this is acceptable.

The required core inductance factor, AL, to achieve the target inductance can be calculated as in Equation 44. The transformer manufacturer uses this factor to gap the core center leg.

Equation 44.

Finally, calculate the required air-gap length lg, based on the required inductance and the core geometry.

Equation 45.

where

μ0 is the permittivity of free-air

μr is the relative permeability of the chosen core ferrite material

ACENTRE is the cross-sectional area of the core center leg

lm is the core average magnetic path length

For the RM10/I core in 3C95 material (chosen for low core loss over a wide temperature range), the required air-gap length is calaulated using Equation 46.

Equation 46.

Typically, the air-gap calculation in Equation 45 underestimates lg, due to flux fringing in the air-gap. The fringing causes the affective area of the air-gap Ag to be somewhat larger than the ferrite core center leg ACENTRE, depending on the gap length. This difference requires an increase in the required air-gap length to get the required inductance, which results in a further increase in fringing. However use Equation 45 to determine an initial value for lg, which can then be used to estimate Ag. For round centre legs, the increase in effective area within the gap can be estimated empirically from Equation 47